Chapter 2.2, Problem 25E

a.

To determine

To calculate:

The correct equation for the following sentence and its solution set:

Carry-on bag can weigh no more than $50pounds$ . The weight of bag is $38pounds$ .

Answer to Problem 25E

The inequality equation for the given condition is written as $38+x\le 50$ and its solution is $x\le 12$

Explanation of Solution

Given information:

Carry-on bag can weigh no more than $50pounds$ . The weight of bag is $38pounds$ .

Calculation:

Consider,

The amount of weight can add to the existent language: $x$

As per the given statement: Carry-on bag can weigh no more than $50pounds$ . The weight of bag is $38pounds$ .

  $38+x\le 50$

So, the inequality equation for the given condition is written as $38+x\le 50$ . Now, need to find its’ solution:

  $38+x\le 50$

Now, subtract $38$ from both sides of above equation:

  $\begin{array}{l}38+x\le 50\\ 38-38+x\le 50-38\\ x\le 12\end{array}$

So, the solution of $38+x\le 50$ is $x\le 12$ .

So, you need to add $x\le 12$ or less than or equal to $12pounds$ weight into bag.

b.

To determine

To explain:

Without overweighing of bag, person can add the following things or not:

Laptop: $9pounds$

Pair of boots: $5pounds$

Answer to Problem 25E

No, by addition of the given things the bag is being overweight.

Explanation of Solution

Given information:

Wight of laptop: $9pounds$

Wight of pair of boots: $5pounds$

As per the part (a) statement: the inequality equation is written for carry-on bag can weigh no more than $50pounds$ . The weight of bag is $38pounds$ .

  $38+x\le 50$

Addition of laptop and pair of boots so,

  $\begin{array}{l}x=9+5\\ x=14pounds\end{array}$

Need to check addition laptop and pair of boots into bag without crossing weight limit as:

  $\begin{array}{l}38+x\le 50\\ 38+x\le 50\\ 38+14\le 50\\ 52\le 50\end{array}$

The weight not satisfies the inequality equation, so it is not a solution. It means that the addition of laptop and pair of boots is not possible.